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I usually start grafting in the first week of May.
I make sure I have drone comb in my drone producing colonies by the middle of April at the latest.
Drones need to be two weeks from emergence to be at peak fertility.
If you graft on say 5th May your queens will be emerging on the 17th May and could take mating flights from the 23rd or 24 of the month.
You need to count back 24 days (drone development egg to emergence) plus 14 days (maturing) from the 23rd and it will be in or around that date when you want your queens to start rearing drone brood.

I tend to use a queenright queenraising method - a demaree - with the brood and grafts in the top box above a queen excluder and a super or two, with the queen in the lower brood box with excluder above. As I don't have a massive demand I generally do 10 grafts at a time, separated by a couple of weeks. This means that if the weather is bad for mating for one batch, it's usually ok for the other. I wait until there are a fair number of drones being produced in other colonies before I start queen-raising. Having said the above, if I have a colony that is queenless for any reason, it can be pressed into service as a queen-raiser during the season.

Adam's rule of thumb: If we say that a full-sized colony can comfortably raise 20 good and well-nourished queens, all things being equal, is that 2 queencells per frame of brood, so a prosperous 5-frame nuc would do 10?

Umm.. no. A full colony has a far greater population than a "prosperous nuc" So my dodge is to use the starter box as only a starter, and it is a box of shook young bees which can cope with 20+ grafts happily and then use Q+ units to finish the cells off.

My nucs are all on Paynes with extenders, I'm going to take the queen out with three frames and then condense all the remaining bees into one nuc box. I'll see if it can handle 20 grafts, if not it's no biggy - I'm not going to run out of eggs and bees for another go.

A paynes nuc with extended is a 12 frame box so the same size as a normal brood box. So to condense you will need to remove 7 frames thus allowing one for the grafts. One of the frames will usually be full - or highly loaded - with pollen. They will definitely be squeezed in! Note that they might be able to handle 20 grafts, the question is whether they can adequately feed 20. You will quite possibly need a feeder on top - say 1/4 litre per day - until the grafts are sealed and in order to ensure that the graft frame is not full with drawn comb by the time the queens are ready, which makes removing them more difficult, you might need to take another frame out and put in one of foundation or partly drawn comb to give them space to work.